Problem with BMesh Vertex Location Precision
The problem is caused by the fact that vertex locations are stored using 32-bit float numbers. This means that there are only 6 significant figures stored, so accuracy takes a dive with large (or very small) coordinate values.

Originally, I had been storing the actual locations of the vertices in the mesh and then moving them all toward the origin of the Blender scene in one go. I had to re-work things so that the localization (bringing closer to xyz=0,0,0) has to happen before the vertex locations are stored in the mesh.